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ComprehensionDIRECTIONS for the question: Go through the graph and the information given below and answer the question that follows.In an election several candidates contested for a constituency. In any constituency, the winning candidate was the one who polled the highest number of votes, the first runner up was the one who polled the second highest number of votes, the second runner up was the one who polled the third highest number of votes, and so on. There were no ties (in terms of number of votes polled by the candidates) in any of the constituencies in this election.In an electoral system, a security deposit is the sum of money that a candidate is required to pay to the election commission before he or she is permitted to contest. Only the defeated candidates (i.e., one who is not the winning candidate) who fail to secure more than one sixth of the valid votes polled in the constituency, lose their security deposits. The following table provides some incomplete information about votes polled in four constituencies: A,B, C and D, in this election. Constituency ABCDNo. of candidates contesting101258Total No. of valid votes polled5,00,0003,25,0006,00,030 No. of votes polled by thewinning candidate2,75,000 48,750 No. of votes polled by the firstrunner up95,000 37,500No. of votes polled by thesecond runner up 30,000% of valid votes polled by thethird runner up 10%The following additional facts are known:1. The first runner up polled 10,000 more votes than the second runner up in constituency A.2. None of the candidates who contested in constituency C lost their security deposit. The difference in votes polled by any pair of candidates in this constituency was at least 10,000.3. The winning candidate in constituency D polled 5% of valid votes more than that of the first runner up. All the candidates who lost their security deposits while contesting for this constituency, put together, polled 35% of the valid votes.1. B, C, D, A2. D, B, C, A3. B, D, C, A4. D, C, B, A |
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Answer» Correct Answer - Option 1 : B, C, D, A EXPLANATION: As it is given in the question that the first runner-up polled 10,000 more votes than the second runner-up in constituency A. Now the first runner-up has got 95000 votes, hence the second runner-up will get 85000 votes. Therefore the remaining votes will be 500000 - 275000 - 95000 - 85000 = 45000 As per the second additional point given, None of the candidates who contested in constituency C lost their security deposit. The difference in votes polled by any pair of candidates in this constituency was at least 10,000 ⇒ The person who got the 5th highest votes must have got greater than 600030/6 = 100006. As it is also given that the difference of votes is greater than 10000, the only possible case is winner, 1st runner up, 2nd runner up, 3rd runner up, 4th runner up must have got 140006,130006,120006,110006,100006 respectively which sums up to exactly 600030. Let the number of votes polled in D be 100x. From 3, The winning candidate in constituency D must have got 15x + 37500 The table now looks like this:
As we have seen in the previous question, candidate D got 175000 votes. The winner got 5% more votes than the first runner up, hence the winner got 0.05 × 175000 = 8750 more votes than the first runner-up. Thus 8750 is the winning margin for constituency D. Moreover margin in the constituency is at least 10000. Hence in the increasing order C will always come after D which is not happening in the third option. Hence that is the correct answer. |
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